Affiliation:
1. School of Mathematics and Statistics , University of Glasgow, University Place, Glasgow G12 8QQ, UK
Abstract
Abstract
We study the cohomology of families of $(\varphi ,\Gamma )$-modules with coefficients in pseudoaffinoid algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify rank-$1$$(\varphi ,\Gamma )$-modules and deduce that triangulations of pseudorigid families of $(\varphi ,\Gamma )$-modules can be interpolated, extending a result of [29]. We then apply this to study extended eigenvarieties at the boundary of weight space, proving in particular that the eigencurve is proper at the boundary and that Galois representations attached to certain characteristic $p$ points are trianguline.
Publisher
Oxford University Press (OUP)
Reference38 articles.
1. Le halo spectral;Andreatta;Ann. Sci. ENS,2018
2. Families of Galois representations and Selmer groups;Bellache;Astérisque,2009
3. Galois representations over pseudorigid spaces;Bellovin;J. Theor. Nombres Bordeaux.
4. Non-Archimedean Analysis
5. The Jacquet–Langlands correspondence for overconvergent Hilbert modular forms;Birkbeck;Int. J. Number Theory,2019
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献